论文标题
关于广义定向半树的加权转移的分析结构
On analytic structure of weighted shifts on generalized directed semi-trees
论文作者
论文摘要
受自然类别的启发，我们定义了广义的定向半树，并在广义定向的半树上构建了加权转移。给定有指导性半树的$ n $ tuple与某些属性相关联，我们将乘以乘法运算符的$ n $组合在希尔伯特空间$ \ mathscr {h}^2（β）正式功率系列的$上。 Under certain conditions, $\mathscr{H}^2(β)$ turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in $\mathbb C^n$ and the $n$-tuple of multiplication operators on $\mathscr{H}^2(β)$ is unitarily equivalent to an $n$-tuple of weighted shifts on广义定向半树。最后，我们展示了两类$ n $ tuple的示例，这些示例可以内在地识别为在广义有向半树上的加权转移。
Inspired by natural classes of examples, we define generalized directed semi-tree and construct weighted shifts on the generalized directed semi-trees. Given an $n$-tuple of directed directed semi-trees with certain properties, we associate an $n$-tuple of multiplication operators on a Hilbert space $\mathscr{H}^2(β)$ of formal power series. Under certain conditions, $\mathscr{H}^2(β)$ turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in $\mathbb C^n$ and the $n$-tuple of multiplication operators on $\mathscr{H}^2(β)$ is unitarily equivalent to an $n$-tuple of weighted shifts on the generalized directed semi-trees. Finally, we exhibit two classes of examples of $n$-tuple of operators which can be intrinsically identified as weighted shifts on generalized directed semi-trees.
